Heat the water (or milk) in a small pan with the butter and salt. When it boils, add the mixed flours all at once, turn the heat down to low and stir rapidly for about 2 minutes until the mixture forms a sticky dough.
Mix in the grated parmesan. Let this cool for 5 minutes and beat the eggs into the dough one at a time with a wooden spoon until the dough comes together. It will be sticky at this stage.
Put this mixture in a pastry bag with a 1/2 inch tip. Boil a pot of lightly salted water and start to squeeze the dough out of the pastry bag into the water, using scissors to cut the dough that comes out into 1/2 inch pieces. Cook the dough until it floats.
Once the gnocchi float, let them cook for 2 minutes longer and then move to a cookie sheet that has some oil on it. Repeat this with the rest of the dough.
Cover the cookie sheet with the dumplings once they are cooled. They will keep in the fridge for 3-4 days.